with \(U_1\)  marginally uniform on \([0,1]\) . These authors employ a D-vine copula, and
show how
estimation using this extended likelihood
can be undertaken
by Bayesian data augmentation, where the values of \(\text{$u$}\)  are generated
in an MCMC sampling scheme. Alternatively,
[1]} show how to estimate the copula parameters using variational Bayes
methods [2]}. These calibrate
tractable approximations to the augmented posterior obtained from
the extended likelihood above. They call this approach “variational Bayes data augmentation”
(VBDA) and
show it is faster than MCMC and can be employed for much larger \(T\)  for many choices of copula.
